Abstract: A self-map on the CW complex is a periodic homotopy idempotent if for some and the iterates and are homotopic. Geoghegan and Nicas defined the rotation index of such a map. They proved that for , the homotopy idempotent splits if and only if , while for , the index divides . We extend this to arbitrary and , and generalize various results related to the splitting of homotopy idempotents on CW complexes and conjugacy idempotents on groups.